Convex Tikhonov regularization in Banach spaces: new results on convergence rates

Tikhonov regularization in Banach spaces with convex penalty and convex fidelity term for linear ill-posed operator equation is studied. As a main result, convergence rates in terms F of the Bregman distance of the regularized solution to the exact solution is proven by imposing a generalization of the established variational inequality conditions on the exact solution. This condition only involves a decay rate of the difference of the penalty functionals terms of the residual.